# Evaluating the quality of Monte Carlo simulations for 3D Ising model

Suppose I have developed a new Monte Carlo method, and I plan to test this method on studying the magnetization of a 3D Ising model at some non-zero temperature $$T$$. The coupling is nearest neighbor, with the coupling strength $$J_{ij}$$ being random at each site. What is the standard way to evaluate the quality of the simulations without an exact solution of the magnetization for comparison, besides using analytical approximations such as the mean-field method or high temperature expansion? In lower dimensions (such as 2D), is there a way to "plant" an Ising instance such that the magnetization can be determined exactly besides the case of the trivial ferromagnetic instance?

• computational science SE might be a better home for this question – By Symmetry May 26 '19 at 12:23
• Related question: physics.stackexchange.com/q/476953 – tpg2114 May 26 '19 at 13:13
• @BySymmetry Taking into account that Computationl Physics is not OT on physics.SE, this is more a question about Computational Physics (or just Physics) than Computational Science. The reason for my claim is that this is not a question about a specific computational algorithm, but it touches the important question "how can we know that numerical results for a specific model of a physical system can be trusted?". – GiorgioP May 26 '19 at 14:53